Which of the following word problems can be solved using the inequality 4x + 16 > 48? Select all that apply. B
Duane has a collection of 16 postage stamps. He will collect 4 new stamps each month. How many months will it take Duane for his stamp
collection to have at least 48 postage stamps?
Jackie wants to save more than 548 to buy a new sweater. She has $16 and will save 54 every week. How many weeks will it take Jackie to save up
more than enough money to buy the sweater?
Kristen is sending a package. She wants the package to have a maximum of 48 ounces. If the package already weighs 16 ounces, how many 4-
ounce ornaments can she place in the package?
Inez is on a game show. She currently has 16 points. If she receives 4 points for correctly answering a question, how many additional questions
must she answer for her score to be a minimum of 48 points?
с
D

We are testing a hypothesis. So, first we identify the null and the alternative hypothesis, then we find the test statistic, and with the test statistic, the p-value is found.

Null and alternative hypothesis:

Claim the the proportion is of 60%, thus, the null hypothesis is:

Test if the proportion is greater than 60%, thus, the alternative hypothesis is:

And the answer to the first question is given by option c.

Classification:

We are testing if the proportion is greater than a value, so it is a right-tailed test.

Test statistic:

In which X is the sample mean, is the value tested at the null hypothesis, is the standard deviation and n is the size of the sample.

0.6 is tested at the null hypothesis:

This means that

Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals.

This means that

Value of the test statistic:

The test statistic is z = 1.837.

p-value:

The p-value of the test is the probability of finding a sample proportion above 0.69, which is 1 subtracted by the p-value of z = 1.837.

Looking at the z-table, z = 1.837 has a p-value of 0.9669.

1 - 0.9669 = 0.0331

The p-value is 0.0331.

Decision:

The p-value of the test is 0.0331 > 0.01, and thus:

a. Fail to reject the null hypothesis

For another example of a problem of a test of hypothesis, you can take a look at: